Environmental regulation and carbon emission efficiency: Evidence from pollution levy standards adjustment in China

China’s economy experienced great growth, which also induces large carbon emission. Facing the target of “Carbon peak, Carbon neutrality” in China, it is vital to improve the carbon emission efficiency. Employing the spatial Difference-in-Differences model, this paper investigates the impact of environmental regulation on carbon emission efficiency with a quasi-natural experiment of Pollution Levy Standards Adjustment in China. Our empirical results show that the environmental regulation can significantly improve the carbon emission efficiency. moreover, two impact channels are explored: green innovation and industrial upgrading. More specifically, the green innovation increases with environmental regulation, and the increased green innovation improves carbon emission efficiency. The industry upgrading increases with environmental regulation, and the increased industry upgrading improves carbon emission efficiency. Finally, in terms of city heterogeneity, we find that the impact of environmental regulation will be more pronounced for larger cities and resource-based cities. Our findings suggest that the environmental regulation must be enhanced for both smaller cities and non-resource-based cities. Moreover, to promote the green innovation of firms, since green innovation is risky and costly, governments should provide more subsidies or grants on corporate green technologies, thus firms will be motivated to invest in green technologies to reduce carbon emission.


Introduction
The rapid growth of greenhouse gas emissions has caused serious issues on the sustainable growth of the world [1,2].China has experienced great economic growth for the last a few decades, however, the tremendous growth also leads to high carbon emission.China's carbon emission has become the largest over the world, total carbon emission has increased from 1.419 billion tons in 1978 to 9.899 billion tons in 2020 [3].This means that China faces enormous pressure to reduce emissions.Facing the pressure of carbon reduction, Chinese government proposes the "Carbon peak, Carbon neutrality" goal aiming at carbon emission reduction.
proves carbon emission efficiency.Finally, the city heterogeneity is considered, we find that the impact of PLSA will be more pronounced for larger cities and resource-based cities.
The reminder of this study is organized as follows: Section 2 provides the literature review, the policy background and research hypothesis are presented in Section 3, Section 4 shows the methods and data, empirical results are analyzed in Section 5, Section 6 presents the robustness check, the discussion is presented in Section 7, the conclusion and policy implications are shown in Section 8.

Literature review
The measurement of carbon emission efficiency has been widely studied in prior literature.Numerous research employ input-output ratio, specifically, the economic output scaled by the carbon emission is used [20][21][22][23], carbon emission efficiency is higher as this indicator is larger.However, the weakness of this indicator lies in the ignorance of some potential factors that may impact the economic output, including industry structure and labor force [23].To overcome this problem, two methods are introduced, including Data envelopment analysis (DEA) and Stochastic Frontier Approach (SFA) [21,[23][24][25][26][27].The concept of these two methods lies in the difference between input and output, more specifically, carbon emission efficiency is computed by the gap between actual carbon emission and expected carbon emission [24,[28][29][30][31].However, these measures are biased due to unobserved heterogeneity among cities, and it differs across different sample size.The measurement error can be ignored in small sample, but it will lead to large estimation bias in large sample [21,23].To relieve this problem, an extended SFA model is proposed [21].With this model, time-varying features, time-invariant features, and city-level heterogeneity in the residuals can be separated simultaneously.
Another trend of studies concentrates on the determinants of carbon emission efficiency, innovative technologies and green innovation have been proved to have great impact on carbon emission performance.Prior literature study the improvement of carbon emission efficiency with new technologies in the manufacturing process, including clean technology and industrial robots [6][7][8][9].In addition, information technology has experienced great development in China, and it has been embedded in manufacturing process and governance activities for large number of firms, evidence also show that digital transformation also improves carbon emission efficiency [10][11][12].Due to intense environmental regulation in China, numerous firms increase their investment in green innovation, and it is proved that the investment in green innovation can significantly improve carbon emission efficiency of firms [13,14].However, the cost of green innovation is extremely high, and it does not bring higher excess returns for firms, thus, the green investment cannot be achieved solely by firms, the role of governments is extremely important in energy saving and emission reduction [32][33][34].Therefore, the subsidies and policy support granted from governments are vital for green innovation of firms in reducing the risk of R&D activities [35,36].
In addition to innovative technologies and green innovation, environmental regulations also have great impact on carbon emission.Numerous policies are implemented by Chinese government to reduce industrial carbon emissions.Among those, command-and-control environmental regulation led by the government still dominates.Although market-based tools such as carbon emissions trading and carbon tax have produced significant emissions reduction benefits [16,17], these benefits have been achieved under the supervision and deterrence of administrative orders and environmental regulations [37].Most scholars emphasize pollution monitoring and administrative controls as the main causes of environmental quality improvements [38,39].Empirical studies based on different countries such as the United States, European Union countries, India, and China have shown that command-and-control environmental regulation is an important driver for reducing environmental pollution and carbon emissions [40][41][42][43].
It can be seen that most studies focus on the impact of green technologies, besides, environmental regulations also show great impact on carbon emission performance.However, previous literature only studies the impact of command-and-control environmental regulation or market-based regulation policies, the Pollution Levy policy has never been investigated, this policy presents the direct punishment on firm's pollutant emission, and the pollution levy standard is adjusted in 2007, which can be employed as a quasi-natural experiment for causal identification.Thus, this paper attempts to investigate the impact of pollution levy standards adjustment on carbon emission efficiency.

Policy background
Among numerous environmental regulation policies, the implementation of pollution levy system is quit longer and with larger range.At the early stage, the pollution levy fee is relatively low and only excess pollution emission will be charged, firms are not motivated for pollution governance.In 2007, State council issued "the comprehensive work plan for energy conservation and emission reduction", all pollution emission will be charged and higher pollution levy standards are required.As a result, from 2007 to 2013, 12 provinces or municipalities in China gradually doubled the levy standards from the original 0.63 yuan/kg to 1.26 yuan/kg.The detail of pollution levy standards adjustment is presented in Table 1.

Research hypothesis
First, the PSLA can impact the carbon emission through the green innovation channel.The PSLA will immediately increase the cost of pollutant emission, thus, to reduce cost, firms are motivated in green innovation, they will invest more in emission reduction and other green technologies [44].The investment in green innovation may conduct two consequences: first, the carbon emission will be reduced due to green technologies [13,14]; second, the innovation activities may lead to higher output [45,46].As a result, the carbon emission efficiency will be improved.Based on the arguments above, we propose the first hypothesis: H1: The environmental regulation will stimulate the green innovation, and the increased green innovation will improve the carbon emission efficiency.Second, the PSLA can impact the carbon emission through industry upgrading channel.The increased pollution levy may cause another effect: the escaping effect.due to the increased cost in pollution cost, firms in high pollution industries may leave this city and move to other cities with lower pollution levy.At the meantime, when the enforcement of environmental regulation is high, governments will prefer firms from tertiary industries to invest in the cities [47].As a result, the PSLA can also promote industrial upgrading.Industrial upgrading leads to a decrease in the share of energy inputs in enterprise production and an increase in the value added of products [48].Therefore, firms can achieve higher output with lower resource inputs, which leads to the improvement of carbon emission efficiency.Based on the above analysis, we propose the second hypothesis.
H2: The environmental regulation will promote the industry upgrading, and the carbon emission efficiency will increase with the industry upgrading.
Overall, both channels will lead to a positive correlation between environmental regulation and carbon emission efficiency, that is, environmental regulation will improve the carbon emission efficiency.
To better understand the relationship between environmental regulation and carbon emission efficiency, a diagram is presented in Fig 1, which is shown as follows:

Spatial difference-in-differences model
The Pollution Levy Standards Adjustment is used as a quasi-natural experiment, and considering the spatial spillover effect [49,50], a Spatial difference-in-differences (DID) model is employed in this paper.
To incorporate spatial factors, three methods are widely used, including Spatial Lag Model (SLM), Spatial Error Model (SEM), and spatial Durbin Model (SDM) [50], but they are slightly different, the spatial lag terms are used in SLM, the spatial lag error terms are incorporated in SEM, SDM combines both SLM and SEM.To ensure the robustness, all three models are applied.
First, SLM specification is given below: where Y it is the carbon emission efficiency, PLSA it denotes implementation of PLSA, d P n j¼1 W ij Y it denotes the spatial lag terms.Second, the SEM specification is given below: where λ denotes the coefficient of spatial auto-correlation error terms.
Finally, the SDM model is specified as: where Con it is the control variables; P n j¼1 W ij PLSA it , and P n j¼1 W ij Con it denote the spatial lag terms of carbon emission efficiency, PLSA, and control variables, respectively.According to current literature [51], due to spatial hysteresis, the point estimation may be biased to estimate the spatial spillover.Thus, the total effect can be divided into direct effect and indirect effect with calculus method.
The SDM model can be transformed into the following equation: The equation above can be expressed by a partial differential matrix, more specifically, taking the k-th independent variable as the example: From Eq 6, the mean of diagonal elements and off-diagonal elements are shown in the partial differential matrix, respectively.The changes of the independent variables in this region denote the direct effect, and the changes in other regions present the indirect effect.

Measurement of variables 4.2.1. Carbon emission efficiency.
As we discussed above, the extended SFA model is used to measure carbon emission efficiency [15].The model specification is given below: where CE i,t presents city-level carbon emission, f(X i,t ; β) is the random frontier function with output determinants X i,t [17,52], μ it denotes the random errors, λ i is the city effect.The inefficiency of continuous, and residual carbon emissions are presented by τ it and γ i , respectively.In addition, the random terms are assumed to be normally distributed as: The persistent carbon emission efficiency (PCEE) is determined by Eq 9, and Eq 10 presents the residual carbon emission efficiency (RCEE).The carbon emission efficiency (CEE) is obtained by the product of PCEE and RCEE.

Environmental regulation.
In this paper, the environmental regulation is measured by the implementation of Pollution Levy Standards Adjustment (PLSA), more specifically, PLSA equals 1 if the observation is after the implementation of PLSA, otherwise it is 0.

Data
The dataset is annual and covers 2004-2015.The carbon emission sample is extracted from the Open-source Data Inventory for Anthropogenic CO2 (ODIAC) [61], other data are obtained from two database: include the Chinese City Statistics Database (CCSD) in Chinese Research Data Services (CNRDS) Platform and the China Urban Statistical Yearbook.Missing values are excluded to form a balanced panel.Finally, our sample is reduced to 238 cities with 2856 observations.The descriptive statistics are presented in Table 3, the carbon emission efficiency has an average of 0.497 with a standard deviation of 0.169.

Spatial autocorrelation test
The spatial correlation of carbon emission efficiency of cities is computed in this paper, and scatterplots of Moran index can reflect the spatial correlation of carbon emission efficiency more visually.The scatterplots of carbon emission efficiency of cities for the years of 2004, 2009 and 2015 are presented in Figs 2-4, respectively.More specifically, the horizontal axis shows the standardized carbon emission efficiency, and the vertical axis presents the spatial lagged values.The coefficients of the primary fit line are significantly positive, it indicates that there is a spatial positive correlation between the urban carbon emission efficiency.Table 4 shows the Moran index of carbon emission efficiency, the Moran index is significantly positive   significantly improves the carbon emission efficiency.Specifically, the implementation of PLSA can induce approximately 2% increase in carbon emission efficiency.The empirical results coincide with our expectation that environmental regulation will improve carbon emission efficiency.Moreover, the coefficients of Gdp and Is are significantly negative, indicating that carbon emission efficiency increases with economic growth.Higher GDP and Is present higher economic growth, and it will lead to higher energy consumption, which further result in higher carbon emission, thus, carbon emission efficiency will be reduced.The coefficient of Gov is negative as well, thus, the government expenditure will reduce the carbon emission efficiency.In addition, the coefficients of Fin are significantly positive, it indicates that more developed financial institutions induce more efficient carbon emission.However, the coefficient of Fdi is insignificant.

Baseline regressions
The estimation results of SDM model show that the implementation of PLSA enhances carbon emission efficiency.Since PLSA pilot cities are distributed across the country and carbon emission efficiency is also spatially correlated, it is necessary to discuss the spatial spillover effects.Table 6 further reports the spatial spillover effects of PLSA on carbon emission efficiency.Specifically, the direct, indirect, and total effects of PLSA on carbon emission efficiency improvement are all significantly positive at the 1% level, thus, PLSA in the city can significantly improve the carbon emission efficiency of this city at 1.7%, and it also significantly improves the carbon emission efficiency of other cities at 3.7%.

Parallel trend test
The results of the parallel trend test are reported Fig 5 .It can be seen that both of the coefficients for two years and one year before the implementation of PLSA are statistically insignificant, this evidence indicates the satisfaction of the parallel trend.In addition, the coefficients for one year, two years, and three years after the PLSA implementation are positive and significant, it suggests that carbon emission efficiency improves after the enforcement of PLSA, and the improvement maintains thereafter.

Impact mechanism of green innovation and industrial upgrading.
To test the impact mechanism, this paper constructs the following mediating effect model to explore the mechanism of the innovative city pilots affecting urban carbon emission efficiency: where Mv it denotes the mediating variable, including green innovation (Green_inn) and industrial upgrading (Iu).Specifically, green innovation is measured by the logarithm of the total number of green invention patents and green applicable patents in city i of year t [62,63].Following current literature [64], industrial upgrading is measured as: r denotes the evolution of the proportional relationship between the three major industries in China from the dominance of the primary industry to the dominance of the secondary and tertiary industries.Larger Iu indicates higher industrial upgrading.Table 7 reports the empirical results for mediation effects, columns 1 and 2 show the green innovation channel, and the industrial upgrading channel is reported in columns 3 and 4, city and year fixed effects are added for all specifications.
For green innovation channel, the coefficient of PLSA in column 1 and the coefficient of Green_inn in column 2 are both statistically significant, it indicates the green innovation channel is significant.Moreover, both coefficients are positive, thus, the implementation of PLSA stimulates green innovation, and carbon emission efficiency increases with the green innovation, which coincides with our first hypothesis.In addition, the coefficient of PLSA is statistically significant in column 2, it indicates that the mediation effect of green innovation is partial.
For industry upgrading channel, the coefficient of PLSA in column 3 and the coefficient of Iu in column 4 are both statistically significant, it indicates the industry up-grading channel is significant.Moreover, both coefficients are positive, thus, the implementation of PLSA stimulates industry upgrading, and carbon emission efficiency increases with industry upgrading, which coincides with our second hypothesis.In addition, the coefficient of PLSA is statistically significant in column 4, it indicates that the mediation effect of industry upgrading is partial.
Overall, the green innovation increases with the PLSA implementation, and the increased green innovation improves carbon emission efficiency.moreover, the industry upgrading increases with the PLSA implementation, and the increased industry up-grading improves carbon emission efficiency.Both channels will lead to the positive correlation between carbon emission efficiency and the implementation of PLSA.

Heterogeneity analysis.
In terms of city heterogeneity, two features are considered: size (Big) and resource (Res).In China, the economy of larger city is more developed, small cities are less developed [65].Then, larger cities are featured with more complex and well-developed industrial system, then, firms with advanced technology will prefer to be located in larger cities, qualified workers also tend to move to larger cities.Thus, the agglomeration of firms and workers will form the scale effect, as a result, the scale effect may differ across different cities [55].Moreover, compared with resource-based cities, non-resource-based cities consume less energy and have lower upside of carbon emission efficiency [66,67].To measure size, Big is equal to 1 if the population of this city is larger than the median of all cities, otherwise, it is 0.Moreover, Res is equal to 1 if the city is resource-based, it's 0 if it is non-resource-based.The empirical results are reported in Table 8, column 1 shows the results for Big, and the results for Res are presented in column 2. Both city and year fixed effects are added for all specifications.
The coefficient of the interaction term between PLSA and Big is significantly positive, it indicates that the impact of PLSA is more pronounced for larger cities.Since larger cities are more developed, thus, the green innovation and industry upgrading will also be more significant.In addition, the enforcement of PLSA will also be more intense in larger cities.As a result, the impact of PLSA will be more pronounced for larger cities.Moreover, the coefficient of the interaction term between PLSA and Res is significantly positive, indicating that the impact of PLSA is greater in resource-based cities.The energy consumption and carbon emission efficiency are much higher for resource-based cities, thus, the impact of PLSA will be larger.

Placebo test
The implementation of PLSA may also impact the carbon emission efficiency of cities without implementation of PLSA, thus, the reliability may be affected.As a result, Monte Carlo simulation is employed as our placebo test, empirical results are presented in Fig 6 .We randomly draw a sample from control group to be the new treatment group, and then we re-estimate the model with DID method.If the coefficients obtained after resampling are normally distributed with a mean of 0, then the results are robust.In this paper, we randomly draw 500 times for resampling, as we expected, the re-estimated coefficients are normally distributed with zero mean.As a result, the improvement of carbon emission efficiency is originated from the PLSA.

Re-estimation using PSM-DID
To ensure that the sample selection bias does not affect the reliability of the conclusions in this paper, we use the difference-in-difference model after propensity score matching (PSM-DID) for re-estimation.For matching, two conventional methods are employed: namely 1:1 nearest neighbor matching and kernel density matching.The results of PSM-DID are shown in Table 8.
According to the results of Table 9, the coefficients of PLSA are 0.016 and 0.023 respectively, and both are statistically significant at 1% level.Thus, the results of PSM-DID coincide with previous findings, it indicates that the PLSA significantly improves carbon emission efficiency.

Re-estimation of different dependent variable
To ensure the robustness of our model, we further use logarithm of GDP per unit of carbon emissions to measure carbon emission efficiency.Empirical results are reported in Table 10, the results of the fixed effects model are presented in column 1, column 2 shows the results of the SLM model, the results of SEM model and the SDM model are presented in columns 3 and 4 respectively.City and year fixed effects are controlled for all specifications.
From Table 10, the coefficients of PLSA are significantly positive for all specifications, thus, the impact of PLSA on the alternative measure of carbon emission efficiency is also positive.The findings are consistent, the implementation of PLSA significantly improves carbon emission efficiency.

Discussions
Regarding our baseline regressions, our empirical results report that the coefficients of PLSA are significantly positive for all specifications, indicating that the implementation of Pollution Levy Standards Adjustment significantly improves the carbon emission efficiency.Specifically, the enforcement of PLSA will result in approximately 2% increase in carbon emission efficiency.Our findings coincide with current research in terms of the effect of PLSA, some scholars also prove that the imposition of pollution fees and technological innovation can help mitigate sulfur dioxide well as chemical oxygen demand emissions [68].From the perspective of carbon emission, our results are in line with previous studies, environmental regulation can significantly reduce carbon emission [69].
Our findings prove that the implementation of PLSA stimulates green innovation, which is also in line with current studies [68].Moreover, we also show that the increased green innovation improves carbon emission efficiency, these results coincide with prior studies in terms of the relationship between innovation and pollution, numerous scholars have analyzed the pollution abatement effect of technological innovation and found that technological innovation contributes to pollution reduction [70,71].
Moreover, we also find that the implementation of PLSA stimulates industry upgrading, and carbon emission efficiency increases with industry upgrading, which coincides with our second hypothesis.From the perspective of environmental regulation and industry upgrading, our empirical results are in line with previous studies.Environmental regulation establishes standards to protect the environment and deal with urgent environmental issues [72].It stimulates the development of the green industry by putting standards and restrictions on resource use, waste management, and pollution [73].These restrictions compel industries to embrace sustainable practices, invest in cleaner technology, and create eco-friendly solutions.Implementing strict environmental regulation stimulates industry upgrading and aids in the shift to a greener economy [74].
In terms of the heterogeneity of cities, our results reveal that the impact of PLSA differs across different cities, this also has been proved in previous studies [69].Cities with different geographical locations, economic development levels, administrative levels, levels of opening up, and environmental protection pressures have different levels of carbon emissions and carbon reduction pressures.According to the marginal effect, the carbon reduction effect in different cities is heterogeneous.

Conclusion
For the last decades, China's economy experienced great growth, which also induces large carbon emission.Facing the target of "Carbon peak, Carbon neutrality" in China, it is vital to improve the carbon emission efficiency.
Employing the spatial DID model, this paper investigates the impact of environ-mental regulation on carbon emission efficiency with a quasi-natural experiment of Pollution Levy Standards Adjustment in China.Our findings show that the environ-mental regulation can significantly improve the carbon emission efficiency.moreover, two impact channels are explored: green innovation and industrial upgrading.More specifically, the green innovation increases with the PLSA implementation, and the in-creased green innovation improves carbon emission efficiency.The industry upgrading increases with the PLSA implementation, and the increased industry upgrading im-proves carbon emission efficiency.Finally, in terms of city heterogeneity, we find that the impact of PLSA will be more pronounced for larger cities and resource-based cities.
The contribution of this paper consists in the following aspects.First, this paper examines the impact of environmental regulation on carbon emission efficiency, especially the environmental regulation with punishment fee, current studies generally focus on command-and-control environmental regulations.Meanwhile, we apply a quasi-natural experiment of the Pollution Levy Standards Adjustment in China for causal identification.Second, we employ spatial DID method due to spatial correlation, this method allows us to identify the spatial spillover effect.Third, we further investigate two possible impact mechanisms: green innovation channel and industry upgrading channel, and the city heterogeneity is also studied.
However, there are still some limitations in this paper.First, our data only contains citylevel sample, not firm-level sample.However, firms are the entities of carbon emission, thus, the conclusion will be more precise if firm-specific data is employed.Second, for less developed cities, the enforcement of environmental regulation should be enhanced to ensure the effect of polices.

Policy implications
This paper highlights the important role of environmental regulation in improving carbon emission efficiency.With our findings, we propose the following policy recommendations: First, from the results of baseline, on average, environmental regulation has significantly positive effect on improving carbon emission efficiency, thus, strengthening the implementation of environmental regulation is indispensable.Precisely, the environmental regulation studied in this paper is pollution levy, thus, environment department should strength the inspection on firm's pollutants emission.
Second, with the implementation of pollution levy, the cost of pollutant emission will be increased.Thus, to reduce cost, firms are motivated in green innovation, they will invest more in emission reduction and other green technologies.Since innovative activities are risky and costly, governments are suggested to provides more subsidies to firms with green innovation.Government subsidies can improve the confidence of firms continuing to engage in green innovation, moreover, corporate financial constraint can be attenuated with government subsidies.
Third, due to the increased cost in pollution cost, firms in high pollution industries may leave this city and move to other cities with lower pollution levy.Thus, the government should consider more policies to attract firms from tertiary industries to invest in the cities, including tax reduction, government subsidies, etc.
Forth, from the results of heterogeneity analysis, the impact of PLSA is more pronounced for larger cities.Larger cities are featured with more complex and well-developed industrial system, then, firms with advanced technology will prefer to be located in larger cities, qualified workers also tend to move to larger cities.Thus, the agglomeration of firms and workers will form the scale effect.In this sense, to attract more qualified workers, governments should promote more policies beneficial for talents, such as housing subsidies, medical services, etc.

Fig 5 .
Fig 5. Results of parallel trend test.The X-axis denotes the window period for PLSA implementation.The Y axis represents the regression coefficient of PLSA implementation.The year before PLSA is implemented as the base period.https://doi.org/10.1371/journal.pone.0296642.g005

Fig 6 .
Fig 6. Results of placebo test.Treatment groups were randomly drawn 500 times in control group by Monte Carlo simulation and DID regression was performed.Plot the obtained regression coefficients as a distribution graph.This figure reports carbon emission efficiency of non-pilot cities as a dependent variable, presenting a normal distribution with an average value of 0. https://doi.org/10.1371/journal.pone.0296642.g006

Table 2 . Variable definition.
at the 1% level from 2004 to 2015.The results show that the carbon emission efficiency of cities in China has a strong spatial correlation.Therefore, spatial factors should be considered in the estimation model.

Table 5
reports the baseline regression results.The results of the fixed effects model are presented in column 1, column 2 shows the results of the SLM model, the results of SEM model and the SDM model are presented in columns 3 and 4 respectively.City and year fixed effects are controlled for all specifications.From Table5, our empirical results show that the coefficients of PLSA are significantly positive for all specifications, it indicates that the Pollution Levy Standards Adjustment policy